Normality through sharing of pairs of functions with derivatives-Reference-Cited by-同舟云学术

Normality through sharing of pairs of functions with derivatives

Published:2023 Issue:20 Volume:37 Page:6709-6717
ISSN:0354-5180
Container-title:Filomat
language:en
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Author:

Charak Kuldeep¹,Kumar Manish¹,Singh Anil²

Affiliation:

1. Department of Mathematics, University of Jammu, Jammu, India

2. Department of Mathematics, Maulana Azad Memorial College, Jammu, India

Abstract

Let F ?M(D) and let a, b and c be three distinct complex numbers. If, there exist a holomorphic function h on D and a positive constant ? such that for each f ? F , f and f ? partially share three pairs of functions (a, h), (b, cf ) and (c, df ) on D, where cf and df are some values in some punctured disk D* ?(0), then F is normal in D. This is an improvement of Schwick?s result [Arch. Math. (Basel), 59 (1992), 50-54]. We also obtain several normality criteria which significantly improve the existing results and examples are given to establish the sharpness of results.

Publisher

National Library of Serbia

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